Is the Acceleration of a Pendulum Zero at its Equilibrium Point in SHM?

In summary, in simple harmonic motion (SHM), the acceleration of a pendulum is 0 when it passes through its equilibrium point because the acceleration of the point on the circle is constant towards the center of the circle. SHM is similar to circular motion and the force is proportional to the displacement, so at the maximum displacement, the force is maximum and at the equilibrium position, the velocity is maximum.
  • #1
jsmith613
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how does it make sense that in SHM the acceleration of a pendulum is 0 when it pases through its eqm point?
surely as SHM is v. similar to circular motion (in terms of the maths) acceleration is constant?

also, how can the force be MAX at eqm point?
 
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  • #2
Acceleration of the point on the circle is constant...towards the centre of the circle.
The point that is executing SHM is the projection of the point onto a diameter.
Effectively you need to look at the circle 'edge on' to see the SHM.
By similar reasoning the velocity is a maximum in SHM at the equilibrium position and is zero at the maximum displacement (amplitude)
The Force is maximum at the maximum displacement (F is proportional to displacement)
 
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FAQ: Is the Acceleration of a Pendulum Zero at its Equilibrium Point in SHM?

What is SHM and how does it relate to the acceleration of a pendulum at its equilibrium point?

SHM stands for Simple Harmonic Motion, which is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium point. The acceleration of a pendulum at its equilibrium point is zero because at this point, the restoring force is equal and opposite to the force of gravity, resulting in no net force and therefore no acceleration.

Does the acceleration of a pendulum remain zero at all points during SHM?

No, the acceleration of a pendulum is only zero at the equilibrium point. As the pendulum swings away from the equilibrium point, the restoring force becomes greater than the force of gravity, causing the pendulum to accelerate back towards the equilibrium point. At the maximum displacement, the acceleration is at its maximum and then decreases as the pendulum swings back towards the equilibrium point.

How does the length of the pendulum affect the acceleration at the equilibrium point?

The length of the pendulum does not affect the acceleration at the equilibrium point in SHM. This is because the acceleration is dependent on the restoring force, which is determined by the force of gravity and the displacement from the equilibrium point. The length of the pendulum only affects the period of the pendulum, or the time it takes to complete one full swing.

Can the acceleration of a pendulum ever be negative at the equilibrium point?

No, the acceleration of a pendulum can never be negative at the equilibrium point. This is because the equilibrium point is defined as the point where the net force is zero. In order for the acceleration to be negative, there would have to be a net force in the opposite direction of the pendulum's motion, which is not possible at the equilibrium point.

How does the amplitude of the pendulum affect the acceleration at the equilibrium point?

The amplitude of the pendulum, or the maximum displacement from the equilibrium point, does not affect the acceleration at the equilibrium point. As long as the amplitude is small and the pendulum is in the linear region of SHM, the acceleration at the equilibrium point will always be zero. However, if the amplitude is large, the pendulum may experience non-linear motion and the acceleration at the equilibrium point may no longer be zero.

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